The schmedley discount department store has about

The schmedley discount department store has about 300 customers shopping in its stores between 9am and 5 pm on Saturdays. In deciding how many cash register to keep open on Saturdays, the manager must consider two factors: Customer waiting time (and associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average of $8 per hour. When only one is on duty, the waiting per customer is about 10 minutes (or 1/6 hour); when two clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes when three clerks are working; and 3 minutes when four clerks are on duty. Schmedley’s management has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately $10 in lost sales and goodwill for every hour of customer time spent in waiting in checkout lines. Using the information provided, determine the optimal number of clerks to have on duty each Saturday to minimize the stores total expected cost. Must show work

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